Are the following statements true or false? Give reasons, quoting any theorems that you need.

(i) There is a sequence of polynomials $P_{n}$ with $P_{n}(t) \rightarrow \sin t$ uniformly on $\mathbb{R}$ as $n \rightarrow \infty$.

(ii) If $f: \mathbb{R} \rightarrow \mathbb{R}$ is continuous, then there is a sequence of polynomials $Q_{n}$ with $Q_{n}(t) \rightarrow f(t)$ for each $t \in \mathbb{R}$ as $n \rightarrow \infty$.

(iii) If $g:[1, \infty) \rightarrow \mathbb{R}$ is continuous with $g(t) \rightarrow 0$ as $t \rightarrow \infty$, then there is a sequence of polynomials $R_{n}$ with $R_{n}(1 / t) \rightarrow g(t)$ uniformly on $[1, \infty)$ as $n \rightarrow \infty$.